def estimate(pheno, lik, K, covs=None, verbose=True):
r"""Estimate the so-called narrow-sense heritability.
It supports Normal, Bernoulli, Binomial, and Poisson phenotypes.
Let :math:`N` be the sample size and :math:`S` the number of covariates.
Parameters
----------
pheno : tuple, array_like
Phenotype. Dimensions :math:`N\\times 0`.
lik : {'normal', 'bernoulli', 'binomial', 'poisson'}
Likelihood name.
K : array_like
Kinship matrix. Dimensions :math:`N\\times N`.
covs : array_like
Covariates. Default is an offset. Dimensions :math:`N\\times S`.
Returns
-------
float
Estimated heritability.
Examples
--------
.. doctest::
>>> from numpy import dot, exp, sqrt
>>> from numpy.random import RandomState
>>> from limix.heritability import estimate
>>>
>>> random = RandomState(0)
>>>
>>> G = random.randn(50, 100)
>>> K = dot(G, G.T)
>>> z = dot(G, random.randn(100)) / sqrt(100)
>>> y = random.poisson(exp(z))
>>>
>>> print('%.2f' % estimate(y, 'poisson', K, verbose=False))
0.70
"""
K = _background_standardize(K)
QS = economic_qs(K)
lik = lik.lower()
if lik == "binomial":
p = len(pheno[0])
else:
p = len(pheno)
if covs is None:
covs = ones((p, 1))
glmm = GLMMExpFam(pheno, lik, covs, QS)
glmm.feed().maximize(verbose=verbose)
g = glmm.scale * (1 - glmm.delta)
e = glmm.scale * glmm.delta
h2 = g / (var(glmm.mean()) + g + e)
return h2
def qtl_test_glmm(
snps,
pheno,
lik,
K,
covs=None,
test="lrt",
NumIntervalsDeltaAlt=100,
searchDelta=False,
verbose=True,
):
"""
Wrapper function for univariate single-variant association testing
using a generalised linear mixed model.
Args:
snps (array_like):
`N` individuals by `S` SNPs.
pheno (tuple, array_like):
Either a tuple of two arrays of `N` individuals each (Binomial
phenotypes) or an array of `N` individuals (Poisson or Bernoulli
phenotypes). It does not support missing values yet.
lik ({'bernoulli', 'binomial', 'poisson'}):
Sample likelihood describing the residual distribution.
K (array_like):
`N` by `N` covariance matrix (e.g., kinship coefficients).
covs (array_like, optional):
`N` individuals by `D` covariates.
By default, ``covs`` is a (`N`, `1`) array of ones.
test ({'lrt'}, optional):
Likelihood ratio test (default).
NumIntervalsDeltaAlt (int, optional):
number of steps for delta optimization on the alternative model.
Requires ``searchDelta=True`` to have an effect.
searchDelta (bool, optional):
if ``True``, delta optimization on the alternative model is
carried out. By default ``searchDelta`` is ``False``.
verbose (bool, optional):
if ``True``, details such as runtime are displayed.
Returns:
:class:`limix.qtl.LMM`: LIMIX LMM object
Examples
--------
.. doctest::
>>> from numpy import dot, exp, sqrt
>>> from numpy.random import RandomState
>>> from limix.qtl import qtl_test_glmm
>>>
>>> random = RandomState(0)
>>>
>>> G = random.randn(250, 500) / sqrt(500)
>>> beta = 0.01 * random.randn(500)
>>>
>>> z = dot(G, beta) + 0.1 * random.randn(250)
>>> z += dot(G[:, 0], 1) # causal SNP
>>>
>>> y = random.poisson(exp(z))
>>>
>>> candidates = G[:, :5]
>>> K = dot(G[:, 5:], G[:, 5:].T)
>>> lm = qtl_test_glmm(candidates, y, 'poisson', K, verbose=False)
>>>
>>> print(lm.getPv())
[[0.0694 0.3336 0.5899 0.7388 0.7796]]
"""
snps = _asarray(snps)
if covs is None:
covs = ones((snps.shape[0], 1))
else:
covs = _asarray(covs)
K = _asarray(K)
if isinstance(pheno, (tuple, list)):
y = tuple([asarray(p, float) for p in pheno])
else:
y = asarray(pheno, float)
start = time()
QS = economic_qs(K)
glmm = GLMMExpFam(y, lik, covs, QS)
glmm.feed().maximize(verbose=verbose)
# extract stuff from glmm
eta = glmm.site.eta
tau = glmm.site.tau
scale = float(glmm.scale)
delta = float(glmm.delta)
# define useful quantities
mu = eta / tau
var = 1. / tau
s2_g = scale * (1 - delta)
tR = s2_g * K + diag(var - var.min() + 1e-4)
start = time()
lmm = LMM(snps=snps, pheno=mu, K=tR, covs=covs, verbose=verbose)
# if verbose:
# print("Elapsed time for LMM part: %.3f" % (time() - start))
return lmm